Boundary output feedback control of a flexible string system with input saturation

In this paper, we consider the control problem of a flexible string system in the presence of input saturation. The dynamics of the string system is represented by the coupled partial differential equation and ordinary differential equations. Firstly, in order to suppress the transverse vibration of the flexible string system, full state feedback control is proposed by introducing a well-defined integral Lyapunov function. An auxiliary system is introduced to handle the effect of input saturation, and the proof for the existence and the uniqueness of the solution of the closed-loop system is presented. The exponential stability is achieved through rigorous analysis without any simplification of the dynamics. Subsequently, for the case that some of system states cannot be directly obtained, output feedback control is developed and uniform ultimate boundedness is guaranteed. Finally, the results are illustrated with numerical simulations for verifying the control performance.